Abstract:

We present a new approach for positioning, pricing and hedging in
incomplete markets, which bridges standard arbitrage pricing and
expected utility maximization.
Our approach for determining whether to undertake a particular
position involves specifying a set of probability measures and
associated floors which expected payoffs must exceed in order that
the hedged and financed investment be acceptable.
By assuming that the liquid assets are priced so that each portfolio
of them has negative expected return under at least one measure,
we derive a counterpart to the first fundamental theorem of
asset pricing.
We also derive a counterpart to the second fundamental theorem,
which leads to unique derivative security pricing and hedging even though
markets are incomplete.
For products that are not spanned by the liquid assets of the
economy, we show how our methodology provides more realistic
bid-ask spreads.